A simple but realistic linear model of production
In this chapter, we use a realistic numerical example in the effort to illustrate most of our empirical findings. Realistic in the sense that the data come from an actual input-output table that of the U.S. economy of 2014. The choice of 2014 from the WIOD instead of the published by the BEA more recent input—output tables of 2018 has to do with the availability of most of the required information. We use two versions of the model, one with circulating capital commonly used in the literature on capital theory and the other with fixed capital, which is a more concrete and, therefore, a more realistic approach. Furthermore, for reasons of simplicity and clarity of presentation, in both models, we do not include the matrices of taxation, depreciation and circulating capital advanced, whose potential presence, as experience has shown, it does not change the results in any significant quantitative and certainly not qualitative way. It is understood that all three matrices, along with the vector of capacity utilization for the adjustment of capital stock matrix to each normal use, could be very easily included (if available) at a later and more concrete stage of analysis.
The remainder of the chapter is structured as follows: Section 7.2 illustrates some of the fundamentals of an input—output analysis and the derivation of the matrix of technological coefficients with the aid of which we determine the relative prices and the equilibrium rate of profit. Section 7.3 expands the analysis by utilizing the aggregated into five sectors input—output table of the U.S. economy of the year 2014 to estimate labor values and their monetary expression, direct prices (DP). Section 7.4 uses the technology matrix along with the money wage and the vector of the basket of wage goods for the estimation of prices of production (PP) within circulating and fixed capital models using two alternative methods for the estimation of the matrix of fixed capital coefficients. Section 7.5 traces the price rate of profit (PRP) trajectories and the wage rate profit (WRP) curves in both models. Section 7.7 applies the eigendecomposition to our aggregated model. Section 7.8 derives the hyper basic industry for illustrative purposes. Finally, Section 7.9 concludes the chapter with a summary and remarks for future research efforts.